The Islanders are moving to Barclays Center in fall 2015, after signing a 25-year lease with the new Brooklyn arena and agreeing to relocate several slap shots west from their current Uniondale, LI, home.

The team, which won four consecutive Stanley Cups between 1980 and 1983, will remain the New York Islanders at the insistence of NHL officials. Arena managers, eager to score a second major tenant for Barclays, owner Charles Wang and borough leaders had no problems with that demand.

“The Islanders are bringing their own silverware, four Stanley Cups to be exact,” Bloomberg said.

Wang said he wanted to keep the team on Long Island, but: “There comes a time when you have to make a decision.”

The Islanders have long sought a new home, to replace the crumbling Nassau Veterans Memorial Coliseum.

Nassau County voters last year rejected a $400 million proposal to overhaul the aging building, where the Islanders have a lease to play until the end of the 2014-15 campaign.

The Brooklyn move also completes a unique sports reunion between the Islanders and Nets. The ABA and NBA “New York Nets” shared the Nassau Veterans Memorial Coliseum with the Islanders between 1972 and 1977.

“The whole world knows Brooklyn is big time and now we have the big league sports to prove it,” said Bloomberg who gave Wang and Snow MetroCards, signifying the Big Apple move.

The new Brooklyn arena holds 17,732 seats for Nets basketball, and arena officials have said it could hold about 14,500 seats for hockey. It would be the smallest arena in the league, but the NHL said it doesn’t have a minimum-seating requirement for its arenas.

The NHL’s smallest seating capacity for an NHL team is 15,015 at the MTS Center in Winnipeg, Manitoba, home to the Winnipeg Jets.

Nassau Coliseum seats 16,234, but the Islanders averaged 13,191 fans per game last season, ranking second to last in the NHL.

Bettman said the arena officials told him, more hockey seats will eventually be added and bring capacity to more than 15,000.

“It [a smaller arena] is not an issue,” Bettman said. “Winnipeg is doing quite well in a building about the same size.”

The Islanders had been scheduled to play a preseason game against the Devils at Barclays, but that was canceled due to the NHL lockout that is currently threatening the season.

Hockey at Barclays will be an odd fit, because the arena wasn’t built with a long, oval-shaped ice rink in mind.

“Who said the rivalry between the Islanders and Rangers couldn’t get any bigger? Well, it just did,” Bloomberg said.

There’ll be very few tickets sold in the south end of Barclays when the hockey is played, creating an unconventional U-shaped seating chart.

Hockey flirted with Kings County decades ago, when the long-folded Brooklyn Americans practiced in the borough and played games at Madison Square Garden.

The Americans wanted to build a new home in Brooklyn. But when World War II broke out, many players joined the military and the franchise folded.

“Seventy years later, the NHL is finally here,” Bettman said.

Pucks are now set to make their Barclays debut in mid-January when Russian teams Dynamo Moscow and SKA St. Petersburg play there in consecutive regular-season games of the Kontinental Hockey League.

The NHL is now stuck in the 39th day of a bitter labor lockout. The season was supposed to have started earlier this month, but all games have been wiped out through at least Nov. 1.

“Things are not progressing as we would like and we’re disappointed,” Bettman said of the lockout.

If owners and players, bickering over the split of league revenue, don’t settle soon, the league might have scale back its normal, 82-game regular season.